Answer:
4 is included in the domain
Step-by-step explanation:
Please answer it now in two minutes
Answer:
[tex] t = 17.3 [/tex]
Step-by-step explanation:
Given ∆TUV,
m < T = 87°
TV = u = 11
TU = v = 14
UV = t = ?
Find t using the Law of Cosines.
[tex] t^2 = u^2 + v^2 - 2*u*v*cos(T) [/tex]
Plug in your values.
[tex] t^2 = 11^2 + 14^2 - 2*11*14*cos(87) [/tex]
[tex] t^2 = 317 - 16.119 [/tex]
[tex] t^2 = 300.881 [/tex]
[tex] t = \sqrt{300.881} [/tex]
[tex] t = 17.3 [/tex] (to the nearest tenth)
Complete the table below to solve the equation 2.5x − 10.5 = 64(0.5x).
Answer:
x = 5 is the solution
Step-by-step explanation:
See the attachment for table values.
f(x) = g(x) for x = 5
The solution to the equation ...
2.5x -10.5 = 64(0.5^x)
is x = 5.
The summer has ended and it’s time to drain the swimming pool. 20 minutes after pulling the plug, there is still 45 000L of water in the pool. The pool is empty after 70 minutes. Calculate how much water was in the pool initially
Answer:
900L per minute
Step-by-step explanation:
1- 70 - 20 = 50
2- in this 50 min the 45000L was drowned
3- 45000L / 50 = 900L
.. ..
Two sides of a square are divided into fourths and another side of the square is trisected, as shown. A triangle is formed by connecting three of these points, as shown. What is the ratio of the area of the shaded triangle to the area of the square? Express your answer as a fraction.
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Explanation:
Let's say this is a 1 by 1 square. The area is 1*1 = 1 square unit. Whatever the area of the triangle is, we divide it over 1 and it will yield the same value as the area of the triangle. In other words, the area of the triangle will be the answer.
Along the top we have 3 ticks to indicate the top segment has been cut into 3+1 = 4 equal parts. The horizontal distance from the the vertical side of the triangle to the peak of the triangle is 3/4 units. This is because we travel 3 ticks out of 4 total. So this is the height when we consider the vertical segment of the triangle to be the base.
The base is 1 unit as it spans the original square's side length
base = 1
height = 3/4
area of triangle = (1/2)*(base*height)
area of triangle = (1/2)*(1*3/4)
area of triangle = 3/8
ratio of triangle area to square area = (triangle area)/(square area)
ratio of triangle area to square area = (3/8)/1
ratio of triangle area to square area = 3/8Answer:
3/8
Step-by-step explanation:
let side of square=x
Area of a square =x^2
height of a triangle= 3x/4 ( 4/4=1/4) since height is only 3x/4 from the square)
( base =x same side as a square)
Area of a triangle=1/2 bh=1/2(x*3x/4)= 3x^2/8
the ratio of shaded triangle to the area= (3x^2/8)/x^2=3x^2/8x^2=3/8
Your family used two full tanks ofgasoline on a road trip. Your car drives about 25 miles per gallon, andthe tank holds 12 gallons of gasoline.a. Find the approximate number of gallons of gasoline used on the trip.b. Find the approximate number of miles you drove on the trip.c. Calculate Assume gasoline costs $1.50 per gallon. How much didyou spend per mile on gasoline?d. Apply You have $20 to spend on gasoline for another trip. The trip is350 miles. You spend the same amount per mile on gasoline as onthe first trip. Do you have enough money for gasoline? Explain.
Answer:
a. 24
b.600
c.36
d. No
Step-by-step explanation:
a.You know the approximate number of gallons is about 24 gallons because each tank holds twelve and your family used 2 of them.
b. You know you drove about 600 miles. This is because you used 24 gallons And each gallon should get you 25 miles. multiply The 2 together to get 600 miles. Or you could set a thing like 1/25=24/x and solve for x.
c. It cost 36 dollars because each gallon is 1.5 and you used 24 gallons so mul the two together to get 36
d. First find the amount of gallons used by dividing 350 by 25 to get 14. Then multiply 14 by 1.5 to get 21. 21 is greater than 20 so you don’t have enough money.
Giải phương trình: 3x^2 + 3x - 6 = 0
Answer:
x=1
x=-2
Step-by-step explanation:
(3x-3)(x+2)
x=1
x=-2
Write 10:5 as a ratio in its simplest form
Answer:
its simplest form for the question is 2:1
Charlie is laying down mulch in his front yard. It takes Charlie 4 minutes to lay down 11 cubic yards of mulch and
16 minutes to lay down 44 cubic yards of mulch.
Plot five data points and the line that represent this direct variation relationship.
Answer with explanation:
Given: Charlie is laying down mulch in his front yard. It takes Charlie 4 minutes to lay down 11 cubic yards of mulch and 16 minutes to lay down 44 cubic yards of mulch.
Here, Time(Independent variable (x)) is directly proportion to the Volume of mulch(dependent variable (y)) lied by Charlie.
Let k be the constant of proportionality, such that
[tex]k=\dfrac{y}{x}[/tex]
For x= 4 and k= 11, [tex]k=\dfrac{11}{4}[/tex]
Required equation: [tex]y=\dfrac{11}{4}x[/tex]
Two points are given in question: (4,11) , (16,44).
Take x= 8 , [tex]y=\dfrac{11}{4}(8)=22[/tex]i.e. point (8,22)
Similarly, for x= 12, y=33 i.e. point (12, 33)
For x= 20 , y= 55 i.e. point (20,55)
Five data points: (4,11) , (16,44), (8,22), (12, 33), (20,55).
Now, we plot these points on graph and join them
Answer:
Here
Step-by-step explanation:
Can anyone help quickly.. explanation is not necessary but would be appreciated, I struggle with this topic and would like to understand it a little bit.
Answer:
38.68 degrees
Step-by-step explanation:
In this equation you are trying to find the degrees using the hypotenuse and opposite. So you have to use the function sin^-1(5/8). Because when using Sin it is opposote ove hypotenuse.
Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule. A(n)=-6+(n-1)(1/5) A)-6,-5 1/5, -4 B)5, -5 1/5,1 4/5 C)-6, -5 2/5, -4 1/5 D) 0, 3/5, 1 4/5
Step-by-step explanation:
An arithmetic sequence is given by relation as follows :
[tex]A(n)=-6+(n-1)\dfrac{1}{5}[/tex]
For the first term, put n = 1. So,
[tex]A(1)=-6+(1-1)\dfrac{1}{5}\\\\A(1)=-6[/tex]
For fourth term, put n = 4. So,
[tex]A(4)=-6+(4-1)\dfrac{1}{5}\\\\A(4)=\dfrac{-27}{5}\\\\A(4)=-5\dfrac{2}{5}[/tex]
For tenth term, put n = 10. So,
[tex]A(10)=-6+(10-1)\dfrac{1}{5}\\\\A(10)=-6+\dfrac{9}{5}\\\\A(10)=\dfrac{-21}{5}\\\\A(10)=-4\dfrac{1}{5}[/tex]
Hence, the correct option is (C).
Answer:
the answer in C)-6, -5 2/5, -4 1/5
first correct answer gets best marks and make it short not super-long please and hurry
Answer:
b > 3 2/15
Step-by-step explanation:
To make it easier to solve convert the mixed fraction to a fraction.
2 3/5 = 13/5
Now, multiply the fraction by 3/3 so that you will have a common denominator.
13/5 × 3/3 = 39/15
Now you solve for b.
39/15 < b - 8/15
39/15 + 8/15 < (b - 8/15) + 8/15
47/15 < b
b > 47/15
Convert the fraction to a mixed fraction to find the answer
47/15 = 3 2/15
b > 3 2/15
Your math teacher caught you text messaging in class, again, so the teacher is making you give a presentation to your math class next week. Your assignment is to analyze the scatter plot that shows people's ages and the number of text messages sent in a day. In 3-5 sentences, explain what you see in the scatter plot below.
Answer: If a scatterplot is included in the assignment
The dots plotted on the graph might closely follow the graph of exponential decline. There is a large number of texts per day by 19-20-21 year-olds, but the number seems to decline exponentially as age increases. With a little work, it may be possible to plot the curve and write an equation to model the decline.
Step-by-step explanation: Look at some graphs of exponential decay. Also consider harmonic and hyperbolic decay. The trend in the data is evident. The main challenge is to look at the data and create an equation that models it.
how would you solve for x here
Answer:
x=-1.30068.......
Step-by-step explanation:
x( 3x^2 - 2) = -4
Distribute
3x^3 - 2x = -4
Add 4 to each side
3x^3 - 2x +4 = 0
Plot using a graphing calculator
x=-1.30068.......
If (Fx) = Square root 4x+9+ 2, which inequality can be used to find the domain of f(x)?
A.Square root 4x is greater than or equal to zero
B.4x +9 is greater than or equal to 0
C. 4x is greater than or equal to 0
D.Square root 4x+9 +2 is greater than or equal to 0
Answer:
Third one 4x+9
Step-by-step explanation:
We khow that any any real number inside the root should be positive
Our root is [tex]\sqrt{4x+9}[/tex]4x+9 shoul be positive wich can be expressed mathematically by:
4x+9≥0
What is the surface area of the regular pyramid? What is the surface area of a square pyramid with a height of 10.4 m and a base side length of 12.4 m? a. 141.4 cm c. 167.4 m b. 162.4 cm d. 188.4 cm
Answer:
A. 141.4 cm
Step-by-step explanation:
The piramide is 141.4cm
Which of the following is an arithmetic sequence?
Answer:
B: 3,0,-3,-6
Step-by-step explanation:
An arithmetic sequence has constant adding or subtracting. In this case, 3 is being subtracted as a constant.
Which of the expressions below can be factored using the difference of squares method?
A. 9x^2 - 16y2
B. 9x-16y
C. 9x^2 + 1672
D. 9x + 16y
Answer: A. [tex]9x^2 - 16y^2[/tex] .
Step-by-step explanation:
A difference of squares problem is factored as :[tex]a^2 - b^2 = (a + b)(a - b)[/tex]For this both terms in the form of squares and a minus sign between them.From all the options only option A has both terms square and they minus sign between them.
Also, [tex]9x^2 - 16y^2= (3x)^2-(4y)^2=(3x+4y)(3x-4y)[/tex]
Here a= 3x and b= 4
Hence, the correct answer is A. [tex]9x^2 - 16y^2[/tex] .
Answer:
A
Step-by-step explanation:
Clothing donations are collected to help a family in need. The function g(x) represents the number of items collected where x is the number of people who donated. Does a possible solution of (60, 10) make sense for this function? Explain your answer.
Answer:
No, it doesn't make sense because the output is not feasible.
Step-by-step explanation:
We are told that the function g(x) represents the number of items collected.
Now, we are also told that x is the number of people who donated.
Now, if we want to consider a possible solution of (60, 10) .
It means, we now have; g(60) = 10
This means that 60 people donated and 10 items were collected.
It doesn't make sense that 60 people donated items and only 10 items were available to be collected.
Thus, we can say that ;
No, it doesn't make sense because the output is not feasible.
Dylan uses the expressions (x2 – 2x + 8) and (2x2 + 5x – 7) to represent the length and width of his bedroom. Which expression represents the area (lw) of Dylan's room?
Answer:
2x⁴+x³-x²+54x+56
Step-by-step explanation:
Given the expression length of dylan room = (x² – 2x + 8) and width = (2x² + 5x – 7), assuming the shap of the room is rectangular in nature, the formula for calculating area of a triangle is given as;
Area of rectangle = Length *Width
Area of the rectangle = (x² – 2x + 8)(2x² + 5x – 7)
Area of the rectangle = x²(2x² + 5x – 7) - 2x (2x² + 5x – 7) + 8(2x² + 5x – 7)
= (2x⁴+5x³-7x²)-(4x³+10x²-14x)+(16x²+40x-56)
expanding the bracket
= 2x⁴+5x³-7x²-4x³-10x²+14x+16x²+40x-56
Collecting the like terms;
= 2x⁴+5x³-4x³-7x²-10x²+16x²+40x+14x+56
= 2x⁴+x³-x²+54x+56
Hence, the expression that represents the area (lw) of Dylan's room is 2x⁴+x³-x²+54x+56
Answer:
2x^4+ x^3 - x^2 + 54x - 56 expression represents the area of Dylan’s room
Step-by-step explanation:
C on edge :)
What is the midpoint of the line segment with endpoints (3.5, 2.2) and (1.5, -4.8)
Answer:
2.5, -1.8
Step-by-step explanation:
½(x¹+x²) ,½(y¹+y²)
½(3.5+1.5) ,½(2.2+(-4.8)
½(5.0), ½(2.2-4.8)
2.5 ,½(-3.6)
2.5, -1.8
Answer: It’s 2.5, -1.3, the other person must’ve misclicked lol
Solve. 8x² + 5 = 35 Round to the nearest hundredth. Enter your answers in the boxes. The solutions are approximately and .
Answer:
x=1.94
x = - 1.94
Step-by-step explanation:
8x² + 5 = 35
Subtract 5 from each side
8x² + 5-5 = 35-5
8x² = 30
Divide each side by 8
8x² /8 = 30/8
x² = 15/4
Take the square root of each side
sqrt( x²) = ±sqrt(15/4)
x = ±sqrt(15/4)
x=1.93649
x = - 1.93649
To the nearest hundredth
x=1.94
x = - 1.94
Answer:
1.94
Step-by-step explanation:
[tex]8x^2+5=35\\8x^2=30 \\x^2=30/8\\x^2=3.75\\\sqrt{3.75} \\[/tex]
≈ ±1.94
Tom and Harry live 24km from each other, which on the map is 5 cm Given that the distance on the map between Harry and the Sea view is 4cm Find the actual distance between Harry and the Sea view.
Answer:
19.5 km
Step-by-step explanation:
the actual distance between Harry and the Sea view:
if 24 km is 5 cm on map
24*4/5= 19.5 km
Find the value of x in the triangle
shown below.
X
85
67
Answer:
x = 28 degrees. 180 degrees in a triangle, 180-85-67=28
Answer:
28 degrees
Step-by-step explanation:
The interior angles of a triangle add up to 180 degrees.
The three angles given are: x, 85, and 67.
Therefore, these three angles must add to 180.
x+85+67=180
Combine like terms on the left. Add 85 and 67.
x+ (85+67)=180
x+152=180
We want to find x. We need to get x by itself. 152 is being added to x. The inverse of addition is subtraction. Subtract 152 from both sides.
x+152-152=180-152
x=180-152
x=28
x is 28 degrees.
A whole number is 6 more than 2 times another number. The sum of the two numbers is less than 50. This can be written in an inequality as x + 2x + 6 < 50, where x represents the smaller number. From the set {13, 14, 15, 16, 17}, the values of x for which the inequality holds true are choise 13,14 13,14,15 15,16,17 16,17
Answer:
5
Step-by-step explanation:
juice is $1.79 for 8-4.23 ounce boxes. What is the unit price
Answer:
I believe the unit price would be 2.39 per unit
Step-by-step explanation:
Suppose that the functions fand g are defined for all real numbers x as follows.
f(x)=x-2
g(x) = 2x+2
Write the expressions for (f-g)(x) and (f.g)(x) and evaluate (f+g)(-1).
Answer:
(f-g)(x)= -x-4
(f.g)(x)= 2x^2 -2x-4
(f+g)(-1) = 3(-1) = -3
Step-by-step explanation:
Hi, to answer this question we have to solve the expressions:
(f-g)(x) = x-2 -(2x+2)
(f-g)(x)= x-2 -2x-2
(f-g)(x) = -2x+x-2-2
(f-g)(x)= -x-4
(f.g)(x) = x-2 (2x+2)
(f.g)(x)= 2x^2 +2x-4x-4
(f.g)(x)= 2x^2 -2x-4
(f+g)(x)= x-2 +2x+2
(f+g)(x) = x+2x-2+2
(f+g)(x)= 3x
(f+g)(-1) = 3(-1) = -3
Feel free to ask for more if needed or if you did not understand something.
Of the 30 people riding the bus to work today, 3 rode a bike to work yesterday, 7 drove a car to work yesterday, and the rest rode the bus to work yesterday. If one of the 30 people riding the bus to work today is selected at random, what is the probability that the person selected will ride the bus to work tomorrow?
Answer:
2/3Step-by-step explanation:
This is a probability question and we have to calculate the sample size.
given the sample size S= 30
3 rode a bike
7 drove a car
20 rode bus
The probability of selecting a person that will take a bus is
[tex]Pr(bus)= 20/30= 2/3[/tex]
Solve the proportion 26/z = 13/22
Answer:
z = 44
Step-by-step explanation:
26/z = 13/22
Using cross products
26 * 22 = 13*z
Divide each side by 13
26/13 * 22 = 13z/13
2 *22 =z
44 =z
Answer:
Z=44
To solve this proportion, you have to isolate z. You have to do what you do on one side of the equal sign to the other as well.
An electronics store is having a back-to-school sale. Blake is interested in purchasing a new computer, and the one he’s been wanting to buy currently has a manufacturer’s rebate of $100. The store is also offering a 10% discount with a school ID, which Blake carries regularly in his wallet. Part A Suppose f(x) = x − 100 and g(x) = 0.9x. Find (f ∘ g)(x).
Answer:
(f ∘ g)(x) = 0.9x - 100
Step-by-step explanation:
Here in this question, we are interested in calculating (f ∘ g)(x)
From the question, we are given;
f(x) = x -100
g(x) = 0.9x
So (f ∘ g)(x) simply means we shall be representing the x in f(x) with the totality of the value of g(x)
Mathematically, what we are saying is that;
Find (f ∘ g)(x) = 0.9x - 100
Help, please!!! What is the mC?